write a go solution for Description:
You are given a rooted tree consisting of n vertices. The vertices are numbered from 1 to n, and the root is the vertex 1. You are also given a score array s_1,s_2,ldots,s_n.

A multiset of k simple paths is called valid if the following two conditions are both true.

- Each path starts from 1.
- Let c_i be the number of paths covering vertex i. For each pair of vertices (u,v) (2<=u,v<=n) that have the same parent, |c_u-c_v|<=1 holds.

It can be shown that it is always possible to find at least one valid multiset. Find the maximum value among all valid multisets.

Input Format:
Each test contains multiple test cases. The first line contains a single integer t (1<=t<=10^4) — the number of test cases. The description of the test cases follows.

The first line of each test case contains two space-separated integers n (2<=n<=2*10^5) and k (1<=k<=10^9) — the size of the tree and the required number of paths.

The second line contains n-1 space-separated integers p_2,p_3,ldots,p_n (1<=p_i<=n), where p_i is the parent of the i-th vertex. It is guaranteed that this value describe a valid tree with root 1.

The third line contains n space-separated integers s_1,s_2,ldots,s_n (0<=s_i<=10^4) — the scores of the vertices.

It is guaranteed that the sum of n over all test cases does not exceed 2*10^5.

Output Format:
For each test case, print a single integer — the maximum value of a path multiset.

Note:
In the first test case, one of optimal solutions is four paths 1to2to3to5, 1to2to3to5, 1to4, 1to4, here c=[4,2,2,2,2]. The value equals to 4*6+2*2+2*1+2*5+2*7=54.

In the second test case, one of optimal solution is three paths 1to2to3to5, 1to2to3to5, 1to4, here c=[3,2,2,1,2]. The value equals to 3*6+2*6+2*1+1*4+2*10=56.. Output only the code with no comments, explanation, or additional text.